C78C78M.14403

Designation: C78/C78M 101

Standard Test Method forFlexural Strength of Concrete (Using Simple Beam withThird-Point Loading)1This standard is issued under the fixed designation C78/C78M; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S. Department of Defense.1 NOTECorrected 9.1.5 editorially in February 2013.

1. Scope*1.1 This test method covers the determination of the flexural

strength of concrete by the use of a simple beam withthird-point loading.

1.2 The values stated in either SI units or inch-pound unitsare to be regarded separately as standard. The values stated ineach system may not be exact equivalents; therefore, eachsystem shall be used independently of the other. Combiningvalues from the two systems may result in non-conformancewith the standard.

1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents

2.1 ASTM Standards:2C31/C31M Practice for Making and Curing Concrete Test

Specimens in the FieldC42/C42M Test Method for Obtaining and Testing Drilled

Cores and Sawed Beams of ConcreteC192/C192M Practice for Making and Curing Concrete Test

Specimens in the LaboratoryC617 Practice for Capping Cylindrical Concrete SpecimensC1077 Practice for Agencies Testing Concrete and Concrete

Aggregates for Use in Construction and Criteria forTesting Agency Evaluation

E4 Practices for Force Verification of Testing Machines

3. Significance and Use3.1 This test method is used to determine the flexural

strength of specimens prepared and cured in accordance withTest Methods C42/C42M or Practices C31/C31M or C192/C192M. Results are calculated and reported as the modulus ofrupture. The strength determined will vary where there aredifferences in specimen size, preparation, moisture condition,curing, or where the beam has been molded or sawed to size.

3.2 The results of this test method may be used to determinecompliance with specifications or as a basis for proportioning,mixing and placement operations. It is used in testing concretefor the construction of slabs and pavements.

4. Apparatus4.1 The testing machine shall conform to the requirements

of the sections on Basis of Verification, Corrections, and TimeInterval Between Verifications of Practices E4. Hand operatedtesting machines having pumps that do not provide a continu-ous loading in one stroke are not permitted. Motorized pumpsor hand operated positive displacement pumps having suffi-cient volume in one continuous stroke to complete a testwithout requiring replenishment are permitted and shall becapable of applying loads at a uniform rate without shock orinterruption.

4.2 Loading ApparatusThe third point loading methodshall be used in making flexure tests of concrete employingbearing blocks that will ensure that forces applied to the beamwill be perpendicular to the face of the specimen and appliedwithout eccentricity. A diagram of an apparatus that accom-plishes this purpose is shown in Fig. 1.

4.2.1 All apparatus for making flexure tests of concrete shallbe capable of maintaining the specified span length anddistances between load-applying blocks and support blocksconstant within 61.0 mm [60.05 in.].

4.2.2 The ratio of the horizontal distance between the pointof application of the load and the point of application of thenearest reaction to the depth of the beam shall be 1.0 6 0.03.

4.2.3 If an apparatus similar to that illustrated in Fig. 1 isused: the load-applying and support blocks shall not be more

1 This test method is under the jurisdiction of ASTM Committee C09 onConcrete and Concrete Aggregates and is the direct responsibility of SubcommitteeC09.61 on Testing for Strength.

Current edition approved Aug. 1, 2010. Published September 2010. Originallyapproved in 1930. Last previous edition approved in 2009 as C78 09. DOI:10.1520/C0078_C0078M-10E01.

2 For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at [email protected]. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.

*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States

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than 65 mm [2.50 in.] high, measured from the center or theaxis of pivot, and should extend entirely across or beyond thefull width of the specimen. Each case-hardened bearing surfacein contact with the specimen shall not depart from a plane bymore than 0.05 mm [0.002 in.] and shall be a portion of acylinder, the axis of which is coincidental with either the axisof the rod or center of the ball, whichever the block is pivotedupon. The angle subtended by the curved surface of each blockshall be at least 0.80 rad [45]. The load-applying and supportblocks shall be maintained in a vertical position and in contactwith the rod or ball by means of spring-loaded screws that holdthem in contact with the pivot rod or ball. The uppermostbearing plate and center point ball in Fig. 1 may be omittedwhen a spherically seated bearing block is used, provided onerod and one ball are used as pivots for the upper load-applyingblocks.

5. Testing

5.1 The test specimen shall conform to all requirements ofTest Method C42/C42M or Practices C31/C31M or C192/C192M applicable to beam specimens and shall have a testspan within 2 % of being three times its depth as tested. Thesides of the specimen shall be at right angles with the top andbottom. All surfaces shall be smooth and free of scars,indentations, holes, or inscribed identification marks.

5.2 The individual who tests concrete beams for acceptancetesting shall meet the concrete laboratory technician require-ments of Practice C1077 including Test Method C78/C78M asa relevant test.

NOTE 1The testing laboratory performing this test method may beevaluated in accordance with Practice C1077.

6. Procedure6.1 Flexural tests of moist-cured specimens shall be made as

soon as practical after removal from moist storage. Surfacedrying of the specimen results in a reduction in the measuredflexural strength.

6.2 When using molded specimens, turn the test specimenon its side with respect to its position as molded and center iton the support blocks. When using sawed specimens, positionthe specimen so that the tension face corresponds to the top orbottom of the specimen as cut from the parent material. Centerthe loading system in relation to the applied force. Bring theload-applying blocks in contact with the surface of the speci-men at the third points and apply a load of between 3 and 6 %of the estimated ultimate load. Using 0.10 mm [0.004 in.] and0.40 mm [0.015 in.] leaf-type feeler gages, determine whetherany gap between the specimen and the load-applying orsupport blocks is greater or less than each of the gages over alength of 25 mm [1 in.] or more. Grind, cap, or use leathershims on the specimen contact surface to eliminate any gap inexcess of 0.10 mm [0.004 in.] in width. Leather shims shall beof uniform 6 mm [0.25 in.] thickness, 25 to 50 mm [1.0 to 2.0in.] width, and shall extend across the full width of thespecimen. Gaps in excess of 0.40 mm [0.015 in.] shall beeliminated only by capping or grinding. Grinding of lateralsurfaces shall be minimized inasmuch as grinding may changethe physical characteristics of the specimens. Capping shall bein accordance with the applicable sections of Practice C617.

6.3 Load the specimen continuously and without shock. Theload shall be applied at a constant rate to the breaking point.Apply the load at a rate that constantly increases the maximumstress on the tension face between 0.9 and 1.2 MPa/min [125

NOTE 1This apparatus may be used inverted. If the testing machine applies force through a spherically seated head, the center pivot may be omitted,provided one load-applying block pivots on a rod and the other on a ball.

FIG. 1 Schematic of a Suitable Apparatus for Flexure Test of Concrete by Third-Point Loading Method

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and 175 psi/min] until rupture occurs. The loading rate iscalculated using the following equation:

r 5Sbd2

L (1)

where:r = loading rate, N/min [lb/min],S = rate of increase in maximum stress on the tension face,

MPa/min [psi/min],b = average width of the specimen as oriented for testing,

mm [in.],d = average depth of the specimen as oriented for testing,

mm [in.], andL = span length, mm [in.].

7. Measurement of Specimens After Test7.1 To determine the dimensions of the specimen cross

section for use in calculating modulus of rupture, take mea-surements across one of the fractured faces after testing. Thewidth and depth are measured with the specimen as orientedfor testing. For each dimension, take one measurement at eachedge and one at the center of the cross section. Use the threemeasurements for each direction to determine the averagewidth and the average depth. Take all measurements to thenearest 1 mm [0.05 in.]. If the fracture occurs at a cappedsection, include the cap thickness in the measurement.

8. Calculation8.1 If the fracture initiates in the tension surface within the

middle third of the span length, calculate the modulus ofrupture as follows:

R 5PLbd2 (2)

where:R = modulus of rupture, MPa [psi],P = maximum applied load indicated by the testing machine,

N [lbf],L = span length, mm [in.],b = average width of specimen, mm [in.], at the fracture, and

d = average depth of specimen, mm [in.], at the fracture.NOTE 2The weight of the beam is not included in the above

calculation.8.2 If the fracture occurs in the tension surface outside of

the middle third of the span length by not more than 5 % of thespan length, calculate the modulus of rupture as follows:

R 53Pabd 2 (3)

where:a = average distance between line of fracture and the nearest

support measured on the tension surface of the beam,mm [in.].

NOTE 3The weight of the beam is not included in the abovecalculation.

8.3 If the fracture occurs in the tension surface outside ofthe middle third of the span length by more than 5 % of thespan length, discard the results of the test.

9. Report9.1 Report the following information:9.1.1 Identification number,9.1.2 Average width to the nearest 1 mm [0.05 in.],9.1.3 Average depth to the nearest 1 mm [0.05 in.],9.1.4 Span length in mm [in.],9.1.5 Maximum applied load in N [lbf],9.1.6 Modulus of rupture calculated to the nearest 0.05 MPa

[5 psi],9.1.7 Curing history and apparent moisture condition of the

specimens at the time of test,9.1.8 If specimens were capped, ground, or if leather shims

were used,9.1.9 Whether sawed or molded and defects in specimens,

and9.1.10 Age of specimens.

10. Precision and Bias10.1 PrecisionThe coefficient of variation of test results

has been observed to be dependent on the strength level of thebeams.3 The single operator coefficient of variation has beenfound to be 5.7 %. Therefore, results of two properly con-ducted tests by the same operator on beams made from thesame batch sample are not expected to differ from each otherby more than 16 %. The multilaboratory coefficient of variationhas been found to be 7.0 %. Therefore, results of two differentlaboratories on beams made from the same batch sample arenot expected to differ from each other by more than 19 %.

10.2 BiasBecause there is no accepted standard for deter-mining bias in this test method, no statement on bias is made.

11. Keywords11.1 beams; concrete; flexural strength testing; modulus of

rupture

3 See Improved Concrete Quality Control Procedures Using Third PointLoading by P. M. Carrasquillo and R. L. Carrasquillo, Research Report 119-1F,Project 3-9-87-1119, Center For Transportation Research, The University of Texasat Austin, November 1987, for possible guidance as to the relationship of strengthand variability.

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SUMMARY OF CHANGES

Committee C09 has identified the location of selected changes to this test method since the last issue, C78 09, that may impact the use of this test method. (Approved August 1, 2010.)

(1) Revised the standard as a dual unit test method.

Committee C09 has identified the location of selected changes to this test method since the last issue, C78 08, that may impact the use of this test method. (Approved July 1, 2009.)

(1) Added new Note 1.

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